Why should water-soluble cutting oil be poured into water and not the other way round?

When water is mixed with oil very quickly, this unstable mix separates into 2 phases, with water on one side and oil on the other.  An emulsifying agent is therefore required to bind these two water and oil phases into a stable mix.

The resulting mix's equilibrium depends on the emulsifying agents being suitably arranged, linking the water and oil molecules together. Whether or not a good balance is achieved is determined when the two liquids are mixed together. Care should therefore be taken and the oil should be poured gradually into the water. The emulsion will remain stable if the oil molecules are dispersed into the water and not the other way round – which would result in something similar to mayonnaise (water molecules dispersed in water).